Track / Stage 4 / 339 of 340 #599 of 2000

Problem 599

AMC 12 late, AIME early

Geometry Difficulty 5.0 Find the answer

4.2. The segment connecting the lateral sides of the trapezoid and parallel to its bases, which are 7 and 17, divides the trapezoid into two parts of equal area. Find the length of this segment.

Your answer

Official solution

Solution. $c=\sqrt{\left(a^{2}+b^{2}\right) / 2}=\sqrt{(49+289) / 2}=13$ .

Answer: 13. (E)

$\begin{array}{|l|l|l|l|l|l|l|} \hline \mathbf{A} & 11 & \mathbf{B} & 11.5 & \mathbf{C} & 12 & \mathbf{D} \\ 12.5 & \mathbf{E} & 13 & \mathbf{F} \\ \hline \end{array}$

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.